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Zh. Mat. Fiz. Anal. Geom., 2008, Volume 4, Number 4, Pages 457–489 (Mi jmag109)  

This article is cited in 4 scientific papers (total in 4 papers)

On contraction properties for products of Markov driven random matrices

Y. Guivarc'h

IRMAR CNRS Rennes I, Universite de Rennes I, Campus de Beaulieu, 35042 Rennes Cedex, France

Abstract: We describe contraction properties on projective spaces for products of matrices governed by Markov chains which satisfy strong mixing conditions. Assuming that the subgroup generated by the corresponding matrices is “large” we show in particular that the top Lyapunov exponent of their product has multiplicity one and we give an exposition of the related results.

Key words and phrases: Lyapunov exponent, Markov chain, martingale, spectral gap, proximal.

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Bibliographic databases:

MSC: 37XX, 22D40, 60BXX, 82B44
Received: 28.03.2008
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Citation: Y. Guivarc'h, “On contraction properties for products of Markov driven random matrices”, Zh. Mat. Fiz. Anal. Geom., 4:4 (2008), 457–489

Citation in format AMSBIB
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\by Y.~Guivarc'h
\paper On contraction properties for products of Markov driven random matrices
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2008
\vol 4
\issue 4
\pages 457--489
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2485240}
\zmath{https://zbmath.org/?q=an:1173.60005}
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\elib{http://elibrary.ru/item.asp?id=12857967}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Deroin B., Dujardin R., “Lyapunov Exponents For Surface Group Representations”, Commun. Math. Phys., 340:2 (2015), 433–469  crossref  zmath  isi  scopus
    2. Gao Zh., Guivarc'h Y., Le Page E., “Stable Laws and Spectral Gap Properties For Affine Random Walks”, Ann. Inst. Henri Poincare-Probab. Stat., 51:1 (2015), 319–348  crossref  zmath  isi  scopus
    3. Guivarc'h Y., Le Page E., “Spectral Gap Properties For Linear Random Walks and Pareto'S Asymptotics For Affine Stochastic Recursions”, Ann. Inst. Henri Poincare-Probab. Stat., 52:2 (2016), 503–574  crossref  zmath  isi
    4. Benoist Y., Quint J., “Random Walks on Reductive Groups”, Random Walks on Reductive Groups, Ergebnisse der Mathematik und Iher Grenzgebiete 3 Folge, 62, Springer International Publishing Ag, 2016, 1–323  crossref  isi
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